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Question: If \(\theta\) is the angle between the vectors **a** and **b**, then \(\frac{|a \times b|}{|a.b|}\)e...

If θ\theta is the angle between the vectors a and b, then ∣a×b∣∣a.b∣\frac{|a \times b|}{|a.b|}equal to

A

tan⁡θ\tan\theta

B

−tan⁡θ- \tan\theta

C

cot⁡θ\cot\theta

D

−cot⁡θ- \cot\theta

Answer

tan⁡θ\tan\theta

Explanation

Solution

Angle between the given vectors a\mathbf{a} and b is θ\theta.

We know that,∣a×b∣∣a.b∣=∣a∣∣b∣sin⁡θ∣a∣∣b∣cos⁡θ=tan⁡θ.\frac{|a \times b|}{|a.b|} = \frac{|a||b|\sin\theta}{|a||b|\cos\theta} = \tan\theta.